US9767345B2 - Systems and methods of constructing three-dimensional (3D) model of an object using image cross-sections - Google Patents
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Abstract
Description
If a projection point on the x axis lies inside a shadow region from the testing light source, it is likely that the projected intersection point is a true intersection point. For example, referring to
Thus, the location of any one of the projection points projected from the intersection point, I, and light sources may be determined based on the other two shadow points and the distance ratios associated with light sources L1, L2 and L3. Because the ratio of the distances between the light sources is predetermined, the complexity in determining the projection point P2 is reduced to little more than calculating distances between the shadow points and multiplying these distances by the predetermined ratio. If the distance between the projection point P2 and the shadow point S1 is larger than the size of the shadow, i.e.,
For example, if there are N light sources, each casting n shadows, the total number of intersection calculations M may then be given as
M=n 2 N(N−1). (Eq. 3)
Because each of these intersection calculations involves multiple operations (e.g., addition and multiplication), the total number of operations, To, may be given as
T o=2n 2 N(2N+1)(N−1). (Eq. 4)
For example, a total number of operations To=2(1)23(2·3+1)(3−1)=84 is required to determine the simplest
T P =n 2 N(N−1)+6Nn 2 (Eq. 5)
The ratio of the required operations to the reduced operations may then be expressed as:
Based on Eq. 6, if the light sources lie along a line or lines parallel to the x axis, the improvement is around an order of magnitude for a small number of lights, whereas the improvement is nearly two orders of magnitude for a larger number of lights.
where j is the total number of intersection regions. For example, there are C3 13=286 combinations in
There are nine additional combinations exist in
Because the minimal solution alone can generate all of the shadows in the scene, each column of the minimal solution matrix has the
Claims (25)
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US14/710,512 US9436998B2 (en) | 2012-01-17 | 2015-05-12 | Systems and methods of constructing three-dimensional (3D) model of an object using image cross-sections |
US15/253,741 US9767345B2 (en) | 2012-01-17 | 2016-08-31 | Systems and methods of constructing three-dimensional (3D) model of an object using image cross-sections |
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US20150242682A1 (en) | 2015-08-27 |
US9697643B2 (en) | 2017-07-04 |
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